The entanglement \(C_{i,i+1}\)  between the nearest two qubits is
plotted as a function of spin site \(i\)  and time \(t\)  in Fig. 3 when
\(J_z=0\) . The three dimensional plot of \(C_{i,i+1}\)  is shown in Fig.
3(a). The counter line of \(C_{i,i+1}\)  is plotted in Fig. 3(b). From
Fig. 3, it is seen that the entanglement \(C_{i,i+1}\)  can be
generated. The entanglement is mirror symmetric about the line of
\(i=30\) . The entanglement \(C_{30,31}\)  generates firstly, then the
entanglement \(C_{29,30}\)  and \(C_{31,32}\)  generate, and so on. The
period of entanglement \(C_{i,i+1}\)  generation is a linear function
of \(|i-30|\) . The notion of diffusive dynamics of pairwise
entanglement in the system can be clearly seen [1]}, [2]}.
The two central neighboring sites are in the state
\(|\uparrow _{N/2}\downarrow _{N/2+1}\rangle \) . Due to the exchange
interaction, they will be entangled after the time \(t=0\) . The
entanglement, initially localized on the two central neighboring
sites of the chain will spread owing to the exchange interaction
[3]}, [4]}.
